Berry's phase in Cavity QED: proposal for observing an effect of field quantization

Geometric phases are well known in classical electromagnetism and quantum mechanics since the early works of Pantcharatnam and Berry. Their origin relies on the geometric nature of state spaces and has been studied in many different systems such as spins, polarized light and atomic physics. Recent works have explored their application in interferometry and quantum computation. Earlier works suggest how to observe these phases in single quantum systems adiabatically driven by external classical devices or sources, where, by classical, we mean any system whose state does not change considerably during the interaction time: an intense magnetic field interacting with a spin 1/2, or a birefringent medium interacting with polarized light. Here we propose a feasible experiment to investigate quantum effects in these phases, arising when this classical source drives not a single quantum system, but two interacting ones. In particular, we show how to observe a signature of field quantization through a vacuum effect in Berry's phase. To do so, we describe the interaction of an atom and a quantized cavity mode altogether driven by an external quasi-classical field.